Evaluation of Distance Functions for the Comparison of Gradient Orientation Histograms

Abstract

Local features of an image are used in many computer vision applications such as object detection and scene matching. The gradient orientation histogram is used by many local features such as Scale Invariant Feature Transform (SIFT), a widely used image local feature. This paper discusses various distance functions that can be used to measure the similarity between the local features described by the gradient orientation histogram. A distance function, based on the quadratic form is proposed for the SIFT descriptor. The state of the art distance functions - Euclidean, Chi-square, Manhattan and the proposed quadratic form based distance function are calculated between the features extracted from the images. Nearest neighborhood ratio strategy is used to find the corresponding features based on the distance measure. Correct matches are estimated using the ground truth transformation function between the images, present in the form of homograph matrix. It is experimentally found that the proposed distance function has an execution time reduced by 21% compared to the Euclidean distance for a similar accuracy performance. The proposed distance retrieves more number of correct matches compared to the modified Earth Mover distance which is fastest among the evaluated distance functions. The future work will be aimed at improving the time taken for computing the distance matrix between the feature sets and a better strategy for computing the matches.